Box Plot Lab Slides Stat Lab: Module 1
Box Plot Lab
Summarizing Data with the Five-Number Summary
The Power of Summary
Imagine reading a 500-page book vs. reading the back cover.
Summarizing helps us:
Simplify massive lists
Find the "typical" value
See the "spread" or variety
The "Big" Data
12, 15, 12, 18, 22, 11, 14, 19, 21, 25, 12, 13, 16, 17, 19, 20...
The Summary
"Most students score around 16, with a range of 11 to 25."
Key Vocabulary
Box Plot
A visual way to display the five-number summary of a data set.
Median
The middle value in an ordered data set.
Quartiles
Values that divide a data set into four equal parts (25% each).
Min / Max
The smallest and largest values in your data set.
Range
The difference between the maximum and minimum values.
Anatomy of a Box Plot
Minimum
Lower
Median
Upper
Maximum
Whisker
Whisker
How to Draw the Plot
Rule: The Box is the Middle 50%
The box always connects Quartile 1 to Quartile 3.
1 Plot your 5 numbers as dots on the axis.
2 Draw a box connecting Q1 and Q3.
3 Draw a vertical line inside at the Median.
4 Add whiskers out to the Min and Max.
Visual Guide
MinQ1MedQ3Max
Whisker Wisdom
What do they mean?
Whiskers represent the extremes of your data. They show the spread outside the middle 50%.
Long Whiskers: Data is very spread out at the edges (high variability).
Short Whiskers: Most data points are huddled close to the center.
Low Variability (Short Whiskers)
High Variability (Long Whiskers)
CHOOSE YOUR TOOL
Dot Plots
Every Point Shown
12345
Best for small data sets
Shows individual frequencies
Gets messy with 1,000s of points
Box Plots
Summary Only
12345
Best for large data sets
Easily compare groups
Hides the individual dots
The Even Set Rule
Finding the Median when N is Even
Ordered Data Set (10 values)
1
2
3
3
4
6
7
8
9
10
Step: Find the Mean of the two middle numbers.
\[\frac{4 + 6}{2} = 5\]
The 25% Distribution Rule
25%
25%
25%
25%
"Each section contains exactly 1/4 of your total data points."
Lab Time!
Task 1: Names
Collect 9 name lengths. This is your ODD data set.
Task 2: Coins
Collect 10 results of "Heads per 10 flips". This is your EVEN data set.
Data Detectives Handout Data Detectives Handout
Assignment: Box Plot Investigation
Researcher Name: ________________________
The Box Anatomy
Every box plot shows 5 numbers (The 5-Number Summary).
MIN
Q1
Q3
MAX
Whisker | Box | Whisker
01 Case 01: Name Game Practice (N=9)
ODD SET
Data Set: 2, 3, 5, 5, 6, 8, 9, 10, 12
Min
Q1
Median
Q3
Max
0 3 6 9 12
02 Case 02: Wing Spans (Even Data)
Median Work: ( ____ + ____ ) / 2 = ________
Data Set: 1, 2, 2, 3, 4, 5, 6, 8, 9, 10
Min
Q1
Median
Q3
Max
0 2 4 6 8 10
03 Case 03: The Tool Showdown
A. Choosing Your Tool
Why would a researcher use a box plot instead of a dot plot for a data set with 10,000 entries?
B. The Concept of Summary
When we "summarize" data, what is our main goal? (Check one)
List every single number in the set
Show the typical value and the spread
C. Interpretation Check
520254095
What percentage of the data is between 5 and 25? _________________
Data Detectives Answer Key Answer Key
Material: Data Detectives Handout
Teacher Reference Only
Case 01: Reading Log (Odd)
Min
2
Q1
4
Avg of 3 & 5
Median
6
Q3
9.5
Avg of 9 & 10
Max
12
Case 02: Wing Spans (Even)
Median Work: (4 + 5) / 2 = 4.5
Min
1
Q1
2
Median
4.5
Q3
8
Max
10
Case 03: The Tool Showdown
A. Choosing Your Tool
"A dot plot with 5,000 dots would be extremely crowded and messy. A box plot summarizes all those points into five clear numbers, making it easier to see the center and spread of large data sets at a glance."
B. Defining Summary
Show typical value and spread
C. Evidence Interpretation
Answer: 50%
Explanation: 25% (Min to Q1) + 25% (Q1 to Median) = 50%
Name Game Example Sheet The Name Game Walkthrough
Case Study: 9 Names (Odd Data Set)
Demo Sheet
1 The Names
MIA
3
AVA
3
SAM
3
JOHN
4
SARAH
5
ROB
6
JESS
7
BEN
3
IZZY
8
2 Sorted Data
3
3
3
3
5
6
7
8
8
Calculations
Minimum 3
Q1 (Med of 3,3,3,3) 3
Median (5th Value) 5
Q3 (Med of 6,7,8,8) 7.5
Maximum 8
Final Plot
MIN/Q1: 3
MEDIAN: 5
Q3: 7.5
MAX: 8
051015
Researcher Note:
My Min and Q1 are both 3! This makes the left whisker disappear entirely.
Whisker Wisdom
Long whiskers show high variability at the edges. No whisker means the extremes are the same as the quartile!
Box Plot Lab Lesson Plan Box Plot Lab: Lesson Plan
6th Grade Math • 90 Minute Block
Unit
Data & Stats
Learning Objectives
Draw a box from Q1 to Q3 to represent the middle 50%.
Identify the 5-number summary boundaries.
Compare variability using whisker length.
Materials Required
• Box Plot Lab Slides (Updated with Construction Steps)
• Data Detectives Handout (Consolidated 1-Page)
• Coins, rulers, and name collection sheets.
Lesson Timeline
0-15m
The Summary Hook: Discuss why 5,000 dots is unreadable. Goal: "Summarize" the mess into 5 key numbers.
15-35m
Direct Instruction: Use Slide 5 to model where the box goes . Explicit rule: The box is a "belt" that holds the middle 50%, connecting Q1 and Q3. Plot the 5 dots first, then "wrap" the box around the middle three.
35-65m
The Lab: Hands-on data collection. Name lengths (Odd) and Coin Flips (Even). Build plots on Activity Sheet.
65-85m
Analysis: Data Detectives Handout. Focus on IQR and 25% distribution interpretation.
85-90m
Closing: Exit Ticket: Sketch a box plot where the median is 10, Q1 is 5, and Q3 is 15.
The "Box" Logic
"The box is the 'meat' of the data. It's the middle 50% that tells us what's typical."
"If students ask where to start the box, say: 'The box starts at Q1 and ends at Q3. The median is the line inside!'"
Common Error
Students often draw the box from Min to Max. Remind them that whiskers are for the edges, and the box is ONLY for the quartiles.
Support Use Q1/Q3 stamps for box boundaries.
Extension How would an outlier affect the box width?
ELL Box = Middle. Whiskers = Edges.
Coin Flip Example Sheet Coin Flip Lab Walkthrough
Case Study: 10 Trials (Even Data Set)
Demo Sheet
1 The Results (Heads)
4
7
5
3
8
6
5
9
4
7
2 Sorted Data
3
4
4
5
5
6
7
7
8
9
Calculations
Minimum 3
Q1 (Med of first 5) 4
Median: (5+6)/2 5.5
Q3 (Med of last 5) 7
Maximum 9
Final Plot
MIN: 3
MED: 5.5
MAX: 9
0246810
Statistical Note:
Because N=10 is even, we average the 5th and 6th numbers (5 and 6) to get 5.5!
The Even-Set Rule
If your data set has an even number of points, the median is the mean of the two middle values. Decimals like .5 are normal!
Box Plot Lab Facilitation Guide Activity Directions
Teacher Facilitation Guide: Names & Coins
1
Task 1: The Name Game (Odd Set)
Step 1: Data Collection
Students find 9 classmates and count letters in first names. Focus: Practice with N=9.
Step 2: Sorting & Calculation
Median is the 5th value. Q1/Q3 are medians of the lower/upper halves. (Since halves are N=4, students average the 2nd and 3rd values of each half!)
2
Task 2: Coin Flipping (Even Set)
Step 1: Experiment
Each student flips 10 times and records Heads. Collect 9 more data points for N=10 total .
Step 2: The Mean Rule
With N=10, the median is the mean of the 5th and 6th numbers . This results in decimals like 4.5 or 5.5 frequently.
Vocabulary Reference
Box Plot
A visual summary of data using a 5-number summary (Min, Q1, Median, Q3, Max).
Median
The numerical middle of an ordered data set.
Quartiles
Values (Q1 and Q3) that divide the data into four equal parts (25% each).
Min / Max
The smallest and largest data points in the set.
Facilitation Scripts
Collecting Data
"Class, as you record names, count the first name only! If you find a 'Sarah' and a 'Max', how will that affect the range of your data?"
Building the Box
"Draw your 5 dots on the number line first. Then build your whiskers and finish with the 'box' around the middle 50%."
Common Issues
Unordered Data
Students often forget to sort. Ask: "Is your minimum actually the smallest number?"
Decimal Medians
Explain that the median is the statistical middle, not necessarily a number that was flipped.
Name and Coin Activity Live Recording Lab
Field Data Logbook
Researcher Name: ________________________
1 The Name Game (Odd Set, N=9)
Collect & Count
Task: Collect 9 first names from classmates. Order the counts least-to-greatest below.
Min
Q1
Med
Q3
Max
0 5 10 15
2 Heads in 10 Flips (Even Set, N=10)
Flip 10x
Task: Flip your coin 10x. Collect results from 9 others. Average the 5th & 6th for median!
Min
Q1
Med
Q3
Max
0 5 10
Identify the IQR (Q3 - Q1) . What does this reveal about the "typical" results of coin flipping in your class?
